Problem 24 · 2019 Math Kangaroo
Stretch
Geometry & Measurement
path-tracingspatial-reasoning
From above, the corridor of a school looks like in the diagram. A cat walks along the dotted line drawn in the middle of the room. How many meters does the cat walk?
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Answer: E — 83 m
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Hint 1 of 2
The cat follows the dashed centre line, so use the middle of each corridor section, not the outer walls.
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Hint 2 of 2
Break the path into the three straight middle-line pieces and add their lengths.
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Approach: add the centre-line segments
- The corridor has three arms; the cat's dashed path runs along the middle of each.
- Bottom arm: the vertical part is 40 − 36 = 4 m wide, so its middle sits 2 m in from the right wall; the centre line runs 36 + 2 = 38 m across.
- Vertical arm: it is 20 m up to the start of the top arm, which is 6 m tall, so the centre line climbs to the middle of the top arm; together this part of the path is 19 m.
- Top arm: from the middle of the vertical arm out to the far end is 26 m.
- Total walked = 38 + 19 + 26 = 83 m (E).
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